We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children's thinking, and learning situations…

The National Council of Teachers of Mathematics (NCTM) poses constructivist ideas in its "Principles and Standards for School Mathematics" (2000). NCTM supports mathematics instruction that takes a developmental perspective; starts and builds on what children know; and leads children to construct relational understanding, problem-solving…

The object of this paper is to present and analyze some observations of the language children in 1st grade (6-7 years old) use when they talk about geometrical objects. The observations are made during a number of encounters with the pupils during one year. The work is part of an ongoing collaboration project between a university college and a…